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 to the see of Rochester, holding with it the deanery of Westminster, and resigning Newington. He led an active life; during his stay at the episcopal residence at Bromley, Kent, his favourite exercise was rowing. He pursued in his new diocese his endeavours for the welfare of the clergy, and had much to do with a movement for augmenting the value of livings in the city of London. Stanley has referred to the pompous style of his chapter orders at Westminster: ‘We, the Dean, do peremptorily command and enjoin.’ The abbey clergy and other officials warmly expressed their gratitude for his attention to their interests. The charge at his second visitation (1800) of Rochester alludes to Priestley's removal to America, ‘the patriarch of the sect is fled.’ In November 1801, at four o'clock in the morning, he made a speech in the lords against the terms of the peace with France. He was translated to St. Asaph on 26 June 1802.

Though in his seventieth year Horsley again addressed himself to the needs of a Welsh diocese. He speaks (ib. p. 333) of a ‘dislike of trouble’ in his natural disposition, and accuses himself of indolence. But he shirked no labour in his public work, and kept up his literary and mathematical activity. He seems, indeed, to have neglected his private affairs. He spent money thoughtlessly, and was deep in debt. His coach was always drawn by four horses. He insured his life for 5,000l., but allowed the policy to lapse two days before his death. In July 1806 he visited his diocese. Intending to visit Thurlow at Brighton, he arrived there on 20 Sept., having heard on the way the news of Thurlow's death on the 12th. On 30 Sept. he was seized with dysentery; it appears from a letter written that day, that he had adopted millennial notions, expecting Napoleon to set up as Messiah. He died at Brighton on 4 Oct. 1806. A funeral service was held at Westminster Abbey; he was buried under the altar at St. Mary's, Newington Butts; the Latin inscription on his monument was written by himself; his remains, with those of his second wife, and daughter by his first wife, were removed to Thorley on 18 July 1876, on the demolition of St. Mary's to make way for a railway. His funeral sermon was preached on 19 Oct. by Robert Dickinson, lecturer at St. Mary's, Newington Butts. Horsley is described as somewhat irritable in temperament and dictatorial in manner; apart from polemics he was notably generous, and so charitable as to be easily imposed upon. His intellectual force was great, and his learning admirably digested. As a speaker and preacher his deep-toned and flexible voice gave due effect to his strong argumentative powers.

Horsley married, first, on 16 Dec. 1774, Mary (d. August 1777), daughter of John Botham, his predecessor at Albury, by whom he had a daughter, who died young, and a son, Heneage (b. 23 Feb. 1776), of Westminster School and Christ Church, Oxford (M.A. 1802), rector of Woolwich, afterwards rector of Gresford, Denbighshire, and prebendary of St. Asaph, ultimately episcopal clergyman at Dundee, and Dean of Brechin (d. 6 Oct. 1847); secondly, Sarah Wright, a protégée of his first wife and in her service; she died without issue on 2 April 1805, aged 53; on her presentation at court, Queen Charlotte noticed her ladylike bearing. There is a portrait of Horsley at the Deanery, Westminster; another is in the possession of Professor Jebb at Cambridge, and a miniature on ivory is in the National Portrait Gallery. A portrait, by James Green [q. v.], was engraved by Meyer; another, by Ozias Humphrey [q. v.], was engraved by James Godby [q. v.], and again by Blood. His episcopal seal is in the possession of the Rev. H. H. Jebb, at Awliscombe, Devonshire.

His publications may be thus classed: Scientific: 1. ‘The Power of God, deduced from the computable instantaneous productions of it in the Solar System,’ &c., 1767, 8vo. 2. ‘Apollonii Pergæi Inclinationum libri duo. Restituebat,’ &c., Oxford, 1770, 4to. 3. ‘Remarks on the Observations made in the late Voyage towards the North Pole,’ &c., 1774, 4to (a letter to Constantine John Phipps [q. v.]). 4. ‘Isaaci Newtoni Opera … Commentariis illustrabat,’ &c., 1779–85, fol. 5. ‘Elementary Treatises on … Practical Mathematics,’ &c., Oxford, 1801, 8vo. 6. ‘Euclidis Elementorum libri priores xiii,’ &c., Oxford, 1802, 8vo. 7. ‘Euclidis Datorum liber,’ &c., Oxford, 1803, 8vo. 8. ‘A Critical Essay on Virgil's … Seasons … With a … Method of investigating the Risings … of the Fixed Stars,’ &c., 1805, 4to. Also papers in the ‘Philosophical Transactions,’ vols. lvii.–lxvi.; astronomical observations corrected for John Robinson's ‘History of Hinckley,’ 1782; and dissertation on the Pleiades in William Vincent's ‘Voyage of Nearchus,’ 1797, 4to. Theological: 1. ‘Providence and Free Agency,’ &c., 1778, 4to. 2. ‘A Charge … to the Clergy of the Archdeaconry of St. Albans,’ &c., 1783, 4to. 3. ‘Letters … in reply to Dr. Priestley,’ &c., 1784, 8vo. 4. ‘A Sermon on the Incarnation,’ &c., 1785, 4to. 5. ‘Remarks upon Dr. Priestley's second Letters,’ &c., 1786, 8vo. (Nos. 2, 3, 4, 5 were reprinted, with supplements, in ‘Tracts in Controversy with Dr. Priestley,’